The win snapped a two-game losing streak for the Eagles (7-4) heading into Wednesday's matchup with Massachusetts, which upset Memphis on Saturday.
Trapani and Raji both went 9-for-13 from the floor and Trapani had four of BC's 10 blocked shots.
Cecil Gresham led the Bulldogs (0-11), who entered the game as one of seven winless teams in the country, with 18 points. It was their 13th straight loss, dating to last season.
Bryant, in its second year in Division I, is coached by Tim O'Shea, who played at BC and worked under Eagles coach Al Skinner at both Rhode Island and BC.
The 46 points by Bryant, playing the first of six straight road games, matched the Bulldogs' season low.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.
The Central Intercollegiate Athletic Association says it won't move its headquarters, its basketball tournament or other conference championships from North Carolina, despite